1

Constraints on the Presence or Absence of Post-Perovskite in the Lowermost Mantle

from Long-Period Seismology

Christine Reif

Department and Earth and Planetary Sciences, University of California Santa Cruz

This study explores the long-period constraints on the presence or absence of the

high temperature and pressure post-perovskite phase in the lowermost mantle. The

ability to detect post-perovskite is examined using three long-period approaches; normal

modes, arrival time variations, and seismic tomography. Normal modes are very

sensitive to 1D perturbations in seismic velocities and density and thus provide a lower

bound on the possible depth extent of post-perovskite of 2680 km depth. Synthetic

seismograms indicate that the theoretically calculated shear velocity jump of 2% would

cause a noticeable bend in the travel-time curve of long-period S wave arrivals. A bend

representing a smaller velocity increase of about 1% is observed in localized areas at

approximately 100 km above the core-mantle boundary. The results of recent

tomographic modeling of temperature and composition in the lowermost mantle are used

to determine if regions are cold or iron enriched enough to be in the post-perovskite

stability field. The long-wavelength iron variations are not large enough to cause lateral

variations in post-perovskite. Due to the steepness the Clapeyron slope, there is a very

narrow range in parameter space in terms of the lower mantle geotherm and transition

depth in which anomalously fast (cold) regions could support the perovskite to post-

perovskite phase change. These collective findings suggest that post-perovskite is not a

global feature, but is likely to be present within 100 km of the CMB in tomographically

fast regions, implying a temperature of range of 2400° K – 2700° K at 2780 km depth.

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1. Introduction

The initial observations that perovskite transforms to what is now known as the

post-perovskite phase [Oganov and Ono, 2004; Murakami et al., 2004; Tsuchiya et al.,

2004a,b] have invigorated not only mineral physics, but also the fields of seismology and

dynamics in the deep Earth. First principles calculations find that the post-perovskite

phase has a 1-2% increase in density, shear velocity, and compressional velocity

compared to perovskite [Tsuchiya et al., 2004a,b; Oganov and Ono, 2004; Stackhouse et

al., 2005a]. These studies indicate that there are two major differences between the

perovskite and post-perovskite structures. The first is that the increase in shear modulus

is much larger than the increase in bulk modulus. This leads to a larger increase in the

calculated shear velocity than the calculated compressional velocity. The second is that

the layered structure of post-perovskite suggests that it is capable of being highly

anisotropic. The implications of post-perovskite anisotropy are explored in detail by

Wookey and Kendall [this volume]. Likewise, Lay and Garnero [this volume] discuss

how post-perovskite may explain many of the reflectors observed in the D’’ region of the

mantle. Dynamic calculations are currently incorporating the effects of a phase change

with the properties of perovskite (Pv) to post-perovskite (pPv) phase change [Nakagawa

and Tackley, 2006] to test the feasibility of maintaining post-perovskite throughout

Earth’s history. Here the focus is on the how the occurrence of post-perovskite in the

lowermost mantle is constrained by long-period seismology.

Long-period seismology is a powerful tool for revealing the large-scale properties

of the Earth’s interior. Observations of very long periods of vibration, known as normal

modes, provide a means to accurately determine the 1D velocity and density profile of

3

the Earth [Dziewonski and Anderson, 1981]. Arrival times of long-period seismic waves

are used to map out 3D velocity structure of the mantle through seismic tomography

[Grand, 1994; Masters et al., 1996; Masters et al., 2000a; Gu et al., 2001; Ritsema and

van Heijst, 2002; Antolik et al., 2003; Montelli et al., 2004; Simmons et al., 2006; Reif et

al., 2006]. Waveform modeling is also used for seismic tomography [Woodhouse and

Dziewonski, 1984; Dziewonski and Woodhouse, 1987; Tanimoto, 1990; Su and

Dziewonski, 1991; Li and Romanowicz, 1995; Megnin and Romanowicz, 2000; Gung and

Romanowicz, 2002; Panning and Romanowicz, 2006]. While normal modes are most

useful for 1D structure, observations of mode splitting can be applied to seismic

tomography to uncover velocity and density anomalies at very long wavelengths

[Giardini et al., 1987; He and Tromp, 1996; Masters et al., 2000a; Ishii and Tromp,

2001, 2004; Beghein, 2002]. The general structure of the Earth’s interior from these

various tomographic models is surprising consistent despite differences in the data and

the inversion methods [Romanowicz, 2003]. Thus, long-period seismology has long-

provided the dynamics, mineral physics, and geochemistry communities a basis with

which to evaluate potential Earth models. Despite its ability to provide direct

observations of the majority of the Earth’s interior, long-period seismology has not yet

been applied to constrain the presence or absence of post-perovskite in the lowermost

mantle.

Since the Earth’s background microseism noise level peaks at roughly 7 and 14

seconds, historically, instruments were designed to record data at long-periods (above 14

seconds) and short-periods (below 7 seconds). With the availability of broadband

stations, the designation of long and short period arises mainly from how the

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seismograms are filtered, although there are many short-period networks that do not have

the bandwidth to make long-period recordings. The advantages of long-period data

include that they occur in a noise low, have simple pulse shapes, and subsequent P and S

phases are not drowned out in the coda of the initial P and S arrivals. However, unlike

short-period seismograms, in which the onset of a phase is often sharply and

unambiguously defined, long-period data have broad pulse shapes making it difficult to

consistently determine the onset of a phase. Therefore, long-period phases must be

compared to similar long-period phases to measure their relative time shifts [Woodward

and Masters, 1991a,b; Grand, 1994; Bolton and Masters, 2001; Ritsema and van Heijst,

2002; Reif et al., 2006].

Early long-period networks include the Worldwide Standardized Seismographic

Network (WWSSN), the Seismic Research Observatory (SRO), the United States

National Seismic Network (USNSN), and the International Deployment of

Accelerometers (IDA). Over time, other networks developed and expanded in the United

States and other countries until their consolidation into the Incorporated Research

Institutions for Seismology (IRIS) in the late 1980’s. The instruments used in the early

networks were designed with a dominant period around 20 seconds, so studies that use

these early data will thus filter the more recent recordings to match the frequency content

of the early stations. The observed seismic phases in these long-period traces are

sensitive to structures with wavelengths of about 200 km. However, the

parameterizations used in global long-period seismic tomography studies are usually

much coarser. The shear and compressional models RMSL –S06 and RMSL – P06 from

Reif et al. [2006] have 4° block spacing with 100 km thick blocks in the upper mantle and

5

200 km thick blocks in the lower mantle are an example of the finest-scale

parameterization that is available to date.

Despite the emphasis often placed on the theory and parameterization of

tomographic models [Li and Romanowicz, 1995; Montelli et al., 2004], the most

important factor in any long or short-period study is the data coverage. Figure 1 shows

the distribution of rays turning at a distance range of 90° - 100°, which corresponds

approximately to depths of 2600 km down to the core-mantle boundary for the entire

IRIS long-period database from 1976 through 2004. The coverage is concentrated under

eastern Eurasia and the central northern Pacific along with smaller regions under the

Cocos plate, the mid-northern Atlantic, and north of Papua New Guinea. While some of

these regions in the central Pacific are sampled by thousands of rays, much of the globe is

untouched. Figure 1 is based on all the available data and does not take into account data

quality. While there are almost 62,000 traces represented in Figure 1, only about 11,000

of those data, or 18%, pass the quality control criteria enabling them to be used in

defining Earth structure. The two most common reasons traces are excluded from

processing is that either their signal to noise ratio is too low or there is a glitch in the

recording. Thus, Figure 1 demonstrates how data availability is the biggest obstacle to

understanding the processes that occur near the core-mantle boundary (CMB).

For a more global analysis, long-period seismology is aided by the addition of

phases other than direct S or P. Long-period phase arrivals can be inspected for the

global distribution of fast and slow time residuals as well as patterns in the travel times

with depth [Bolton and Masters, 2001]. However, the most common application is the

collection of long-period travel times for mantle tomography. The core-reflected phase

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ScS, which arrives at shorter distances of 40° - 70°, greatly improves CMB coverage.

Short period studies of precursors to ScS arrivals are confined to well-sampled regions as

they rely on stacking seismic records [Russell et al., 1999; Avants et al., 2006].

However, measuring the long-period arrival times of these phases provides constraints on

the longer-wavelength features near the CMB. In fact, the combination of direct S and

ScS-S provides almost global coverage at the CMB, such that tomography models which

incorporate these two phases (as well as any additional phases such as SKS) are

reasonably resolved. Since the liquid outer core does not transmit shear energy, S waves

reflect off the boundary as if it were a free surface, however, P waves do not have a high

impedance contrast across the boundary making PcP a low amplitude phase that is not

observed in individual seismograms. Therefore, the P coverage at the CMB is mostly

confined to the zones indicated in Figure 1. Consequently, we have a better

understanding of the shear velocity structure than the compressional velocity structure

near the CMB. Due to the greater reliability of shear velocity structure and the greater

change in shear velocities from Pv to pPv, this study concentrates on the analysis of S

waveforms and shear velocity models.

There are essentially three possibilities for the existence of post-perovskite. 1)

Post-perovskite is a global feature of the lowermost mantle. 2) Post-perovskite does not

exist in the lowermost mantle. 3) The presence of post-perovskite varies laterally at long

or short scales in the lowermost mantle. Here we perform a series of hypothesis tests to

investigate these possibilities and converge on a range of physical parameters for which

post-perovskite could exist and explain observations of long-period data. First the

probability that post perovskite exists as a ubiquitous layer is analyzed using normal

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modes. Then the predicted effects of the phase change on long-period waveforms are

compared to observed waveforms in well-sampled fast and slow regions of the lowermost

mantle. Finally, thermo-chemical models of the lower mantle are explored using a series

of possible geotherms and transition depths to identify the conditions for which

anomalous regions can be best explained by the presence of post-perovskite.

2. Normal Modes

Very large earthquakes excite standing wave vibrations, or normal modes,

throughout the Earth causing the Earth to “ring like a bell” for periods of hours to days.

The spheroidal and torodial patterns of normal mode energy can be expressed in terms of

spherical harmonics,

�

Sl

mand

�

Tl

m , where

�

l is the degree of the harmonic and

�

m is the

order,

�

m = 2l +1. In theory, the spheriodal energy (

�

S) should only appear on the vertical

and radial components of a seismogram and likewise the torodial energy (

�

T ) should only

be present on the transverse component of the seismogram. However, there can be

coupling between the two due to rotation and 3-D structure [Woodhouse, 1980; Masters

et al., 1983] [for a more complete summary see Masters and Widmer, 1995].

Normal modes are observed as peaks in the frequency domain of a seismogram.

In the case of an spherically symmetric Earth, all of the

�

2l +1 singlets should occur at the

same frequency forming a peak called a mulitplet. In the real Earth, additional peaks are

observed that are offset from the predicted mulitplet peaks, indicating that the mulitplet is

being separated into individual singlets, which is known as mode splitting [Backus and

Gilbert, 1961; Pekeris et al., 1961]. The observation of mode splitting is analogous to

the observation of reflected phases in travel-time seismology as they both reveal

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information on the 3D variations in Earth structure. The measurement of these splitting

frequencies can be mapped into 3D velocity and density structure for the earth [Jordan,

1978; Woodhouse and Dahlen, 1978; Giardini et al., 1987]. Many studies have used

normal modes splitting measurements to produce tomographic models of the velocity and

density structure of Earth’s interior (see introduction). However, this can only be done at

even order degrees since the structure contained in the odd order degrees is averaged out

over the many passes the energy takes as it traverses the globe [Masters and Widmer,

1995]. While normal mode data are limited in their ability to resolve 3D structure, they

are optimal for constraining the 1D properties of the earth since they are unaffected by

earthquake location and timing errors, provide the most reliable density estimates, and are

highly sensitive to even very small perturbations in the radial velocity and density profile

of the earth. Here we examine the constraints that normal modes provide on the possible

depth extent of post-perovskite

To familiarize the reader with the lateral and depth sensitivities of certain normal

modes, Figure 2 shows the lower-mantle sensitive modes

�

S2

m and S4

m as functions on a

sphere (top) and their shear (solid line) and compressional (dashed line) sensitivity

kernels with depth (bottom). The value of

�

l indicates the number of zero crossings in

latitude and the value of

�

m indicates the number of zeros crossings in longitude. To

conserve space, only the patterns for

�

!1" m " 1 are shown. As the value of

�

l increases,

the pattern on the sphere becomes more complex. The Earth resonates with the same

spherical harmonic pattern at specific frequencies. The notation

�

nSl indicates the

overtone index,

�

n , for a given harmonic degree,

�

l. The overtone index increments by

one for each frequency at which the mode is predicted to occur. The fundamental mode

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0Sl is the lowest frequency mode occurrence and modes that occur at higher-order

frequencies are termed overtones. The fundamental modes typically represent surface

wave behavior while the overtones are equivalent to body waves. Mode energy may not

be observed if it is trapped at an interface such as the CMB (i.e. a Stonely wave).

However, at low l , the fundamental modes exhibit some Stonely wave behavior and thus

are sensitive to structure near the CMB but are still observed (Figure 2). Thus, it is

mainly these low harmonic degree, low overtone index modes that provide constraints on

the radial velocity and density structure near the CMB.

The modes shown in Figure 2 are mainly sensitive to structure on the mantle side

of the core-mantle boundary, however a tiny fraction of the 0S2

shear energy is in the

inner core and a small amount of 0S4

compressional energy is present in the top of outer

core. It is this leakage of energy that makes it difficult for normal modes to constrain the

one-dimensional velocity and density structure at the core-mantle boundary. Figure 3

shows the ability of the normal mode structure coefficients compiled by Masters et al.

[2000b] to resolve shear velocity (top), compressional velocity (middle), and density

(bottom) structure throughout the mantle. The width of the resolution kernel as function

of radius in the mantle is plotted for perturbations of 0.1%, 2%, and 5%. The width of

the resolved velocity and density perturbations decreases as the uncertainty increases.

For instance, given a 2% radial perturbation in shear velocity at the CMB (Figure 3: top,

solid line), the normal modes can detect the anomaly within a zone 350 km wide. This

value drops to 200 km width at around 200 km above the CMB. The density resolution is

similar such that a 2% anomaly could be detected within a zone 180 km wide at 200 km

above the CMB. Therefore, the theoretical estimates of a shear velocity and density

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increase on the order of 2% for the perovskite to post-perovskite transition would be

resolvable within a 2% uncertainty down to a depth of about 200 km above the CMB.

Since normal modes are uniquely suited for constraining the 1D structure of the

Earth, we can use them to explore possibilities (1) and (2) that post-perovskite either

exists everywhere or not at all in the lowermost mantle. The errors on the pressure

(hence depth) of the Pv to pPv transition are on the order of 5 - 10 GPa or 100 – 200 km.

Theoretical and experimental studies [Akber-Knudsen et al., 2005; Tateno et al., 2005]

have indicated that the inclusion of Al in pPv structure can broaden the phase loop of the

perovskite to post-perovskite transition, decreasing the amplitude (hence detectability) of

reflections from the transition. Considering these uncertainties, the normal modes find

that the upper bound on the height at which post-perovskite can exist as a global layer is

about 200 km above the CMB. It was originally proposed that increasing Fe shallows the

transition [Mao et al., 2004], however Hirose et al. [2006] suggest that the difference

may lie in the use of different pressure scales. The experimentally determined transition

of Pv to pPv for a pyrolite composition [Murakami et al., 2005] and a MORB

composition [Hirose et al., 2005] using the Au pressure scale [Tsuchiya, 2003] occurs at

about 110 GPa for an adiabatic geotherm [Williams, 1998] or a depth of about 350 km

above the CMB. Phase transitions measured for pure MgSiO3 using the Pt pressure scale

[Holmes et al., 1989] or the Jamieson [1982] Au pressure scale occur at depths within

200 km of the CMB [Murakami et al., 2004; Oganov and Ono 2004; Ono and Oganov,

2005]. The studies corresponding to a deeper transition are consistent with the majority

of observations of reflectors in D’’ [Wysession et al., 1998] and the normal modes. In

summary, if the post-perovskite phase is the dominant phase at some depth in lowermost

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mantle, it must be confined below 150 – 200 km above the CMB or else it would be

detected by the free oscillations of the earth. Since it has been demonstrated that the

normal modes have reduced sensitivity near the CMB, it is necessary to examine the

long-period waveforms for signs of a global Pv to pPv transition at depths greater than

200 km.

3. Long-Period Waveforms

The majority of evidence thus far for a Pv to pPv transition in the lowermost

mantle has come from short-period studies that find discontinuous jumps in seismic

velocity within a couple hundred kilometers of the CMB [Thomas et al., 2004a,b; Sun et

al., 2006; Hutko et al., 2006]. These short-period studies use stacking procedures to see

if there is any coherent signal that can be related to reflections off of a seismic

discontinuity. This type of methodology can be applied in locations where there is

enough data redundancy to allow small amplitude reflections to emerge out of the

background noise level. Reflectors were first observed in the D’’ region by Lay and

Helmberger [1983]. Since then the majority of reflectors have been identified in fast

regions that are thought to be associated with ponding of subducted lithospheric slabs at

the CMB, these reflectors are often explained in terms of chemical heterogeneity [see

Wysession et al., 1998 and Lay and Garnero, this volume, for a summary and further

details]. When the Pv to pPv transition was first discovered to have a steep, positive

Clapeyron slope, it seemed probable that the reflections observed in these fast, hence

cold, regions were due to the cold thermal anomaly of the slab placing the region in the

pPv stability field. This interpretation suggests that fast regions at the CMB are fast not

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only because they are cold, but also because of the transition to pPv. Likewise, slow

regions are slow because they are too warm for pPv to exist and possibly chemically

distinct as well. This simplistic view has been challenged lately as velocity jumps in the

D’’ region have been identified in seismically slow regions [Avants et al., 2006; Lay and

Garnero, this volume]. For pPv to exist in these slow regions there must be strong

chemical heterogeneity to overcome the effects of the increase in temperature. Thus, it

would be advantageous if long-period seismology could provide a comprehensive

understanding of the relation between pPv and fast and slow areas at the CMB.

In this section the predicted effect of post-perovskite on long-period waveforms is

determined and compared to actual data. Long-period waveforms of phases such as S, P,

and ScS are too broad for reflections from an interface with a small velocity contrast to be

detected. However, the velocity increase associated with the phase transition will result

in a distortion of the long-period travel-time curve. The arrival picks from a series of

synthetic seismograms are shown in Figure 4. The synthetics were calculated based on

actual ray paths turning in a 4° diameter circular bin in the north-central Pacific

(longitude = 190, latitude = 21). The traces range from distances of 80° - 100° at a

roughly 0.2° interval. This region was chosen due to the high concentration of turning

points in the lowermost mantle (see Figure 1). The synthetics of the observed seismic

traces are computed using normal mode summation. The left hand plot of Figure 4 shows

the arrival picks of seismograms computed with the isotropic PREM [Dziewonski and

Anderson, 1981] 1D reference Earth model. The arrival picks on the right hand side are

from seismograms computed using a modified version of PREM, which has a 2% jump in

shear velocity and density and a 1% jump in compressional velocity 180 km above the

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CMB. This depth was chosen as it is deep enough to be within the uncertainty of the

normal mode data and is consistent with the majority of experimental and theoretical

studies regarding the depth of the Pv to pPv transition [Hirose, 2006]. Both sets of picks

are aligned on the predicted PREM arrival. The shear velocity jump in the altered PREM

causes the S wave pulses to arrive earlier than those predicted by PREM for distances

beyond 92°. This bend in the travel-time curve is easily detectable and would be

apparent in observed seismograms where there are numerous turning rays. It is important

to note that the phase transition would have to occur at a depth high enough above the

CMB such that the bend in the travel-time curve could be detected. Therefore, even if a

bend in the travel-time curve is not observed, pPv could still exist at depths within 30 km

of the CMB. However, due to the thermal boundary layer, it is most likely too hot for

pPv to be stable so close to the CMB.

The following is a description of the procedure for the global analysis of long-

period seismograms. (1) Gather all arrival time picks corresponding to rays in the Reif et

al. [2006] catalog of long-period S arrivals that turn in a distance range of 80° – 100°. (2)

Create separate files of picks for rays turning within a 4° diameter circular bin at the

CMB. (3) Visually inspect the picks bin by bin for a negative (fast), a positive (slow), or

no observed bend in the travel-time curve. The resulting map of fast (blue) and slow (red)

bins is shown in Figure 5. The bins in which no bend is detected are left white. An

interesting feature of Figure 5 is the small number of bins for which a bend in the travel-

time curve can be detected. Figure 6 shows the actual picks in bins with fast, slow, and no

bend in the travel time curve. It is representative of the dataset that the magnitude of the

move-out of the travel-time curve for the slow picks is greater than that of the fast picks.

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Compared to the synthetic picks, the slow bend represents a velocity decrease on the

order of 2%, but the fast bend is only on the order of 0.5 – 1%. The distance at which the

picks veer fast or slow is similar for both the fast and slow picks at around 96° or 100 km

above the CMB. The large number of null observations indicates that if pPv does exist in

the lowermost mantle it is likely a very localized phenomenon.

The analysis of the travel-time curves shows that fast regions within 100 km of

the CMB are observed under northern Eurasia and the Cocos plate (Figure 5), which are

also fast regions in tomographic models (Figure 7). The observation of a further increase

in velocity near the CMB in tomographically fast regions supports the idea that the cold

thermal anomaly of the subducted slabs causes the transition of Pv to pPv. However, fast

travel-times are also observed in seismically slow regions such as the central Pacific

where slow travel-times are also observed. Avants et al. [2006] also observe sharp

increases in velocity within the tomographically slow region to the south of Hawaii.

Therefore, the observation of relatively fast material in these predominantly slow regions

may reflect local temperature and/or chemical anomalies that are favorable for the Pv to

pPv transition. Thus, the long-period travel-times find that post-perovskite is not a global

feature within 200 km of the CMB, but can explain observed increases in shear velocity

in a variety of localized regions of lowermost 100 km of the mantle. This demonstration

that pPv is likely present in the well-sampled fast regions of the lowermost mantle

implies that it may be present in the majority of the anomalously fast regions of the

CMB. Therefore, the ability of seismic tomography to constrain the presence of post-

perovskite is explored in the next section.

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4. Seismic Tomography

Since the long-period waveforms suggest that post-perovskite may contribute to

the broad fast velocity anomalies in the lowermost mantle, it is necessary to investigate

tomographic models for their ability to predict the occurrence of post-perovskite.

Tomographic models reveal where seismic wavespeeds are slower or faster than the

average speed at that depth. Since the late 1970’s, tomographic models have imaged

slow shear and compressional anomalies beneath the Pacific and Africa and fast

anomalies in the circum Pacific near the CMB [Sengupta and Toksov, 1976; Dziewonski

et al., 1977; Clayton and Comer, 1983; Dziewonski, 1984; Hager et al., 1985]. With the

finding that post-perovskite is a seismically fast phase, it is necessary to evaluate whether

or not the fast anomalies near the CMB are associated with the phase transition. A recent

study by Helmberger et al. [2005] converted the Grand [1994] model into depth

variations of the Pv to pPv transition by converting of shear velocity to temperature and

using the 6 MPa/K Clapeyron slope of Sidorin et al. [1999]. Here a different approach is

used in which depths of the phase transition and geotherms are explored by using thermo-

chemical models based on seismic data to reveal if fast anomalies in the lowermost

mantle can be explained by the presence of post-perovskite.

Recent mineralogical studies have developed equations of state for perovskite

[Trampert et al., 2004, Mattern et al., 2005, Li and Zhang, 2005]. These equations of

state are used to extrapolate seismic velocities and density to lower mantle temperature

and pressures. By altering the initial conditions, such as temperature or molar volume of

iron, and performing a series of extrapolations, the changes in seismic velocity with

temperature and composition can be determined [Trampert et al., 2004; Li, submitted].

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The dominant signals in the lowermost mantle are the variations in shear velocity [Reif et

al., 2006], Figure 7. Therefore, interpretations of lowermost mantle thermo-chemical

structure will be most dependent on the values of the change in shear velocity with

temperature (dlnVs/dT) and the change in shear velocity with composition (dlnVs/dX).

Using these derivatives, a tomographic inversion can be reframed to solve for thermo-

chemical anomalies [Trampert et al., 2004; Reif et al., 2005]. The values of dlnVs/dT

from the Trampert et al. [2004] study are much less than those of Li [submitted] resulting

in very different thermo-chemical models. Essentially, shear velocity anomalies are

mapped into variations in iron in the Trampert et al. [2004] model due to larger values of

dlnVs/dXFe than dVs/dT, while shear velocity is mapped into variations in temperature in

the Reif et al. [2005] model since dlnVs/dT is greater than dlnVs/dXFe. This study is not

meant to evaluate which set of sensitivity values is the best representative of the lower

mantle, but to use them to construct end-member models of temperature and composition.

The Reif et al. [2005] model is based on an extensive body wave dataset as opposed to

the model of Trampert et al. [2004] which has only 3 layers in the lower mantle and

coarser lateral parameterization since it is based purely on normal mode data. To aid in

comparison, the sensitivities used by Trampert et al. [2004] are applied to the Reif et al.

[2005] dataset of S and P body waves as well as measurements of normal mode splitting

[Masters et al., 200b] to invert for lowermost mantle thermo-chemical structure. The

resulting two models of lowermost mantle temperature and composition are shown in

Figure 8. The top two rows contain the deepest layers of the model dominated by

temperature variations [Reif et al., 2005], hereafter referred to as Model A, and the

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bottom two rows contain the deepest layers of the model dominated by variations in the

mole fraction of iron (based on Trampert et al. [2004]), hereafter referred to as Model B.

Models A and B share the characteristic that the pattern of heterogeneity in the

dominant parameter reflects the overall pattern of the shear velocity model. In places

such as the central Pacific where S and P velocities are not consistent with purely thermal

or chemical effects [Masters et al., 2000a; Ishii and Tromp, 2004], additional

heterogeneity is required in the other parameters to explain the data. For instance, in

Model B the iron variations look very much like the shear velocity anomalies, but under

the central Pacific and Africa, high temperatures accompany the increases in iron in order

to explain the data. One main difference in the models is that little structure is present in

the iron map of Model A and the perovskite map of Model B, which is due to the

different weighting of the sensitivities. Another important difference is the change in

magnitude of the iron and temperature variations from Model A to Model B. Since

Model A is dominantly sensitive to temperature, a smaller change in temperature is

necessary to create the same change in shear velocity compared to Model B. Likewise,

the magnitude of the iron variations in Model B is smaller than that in Model A. The

counter-intuitive result is the model that is less sensitive to a given parameter will have

higher magnitude fluctuations in that parameter. Thus, although Model A is dominantly

sensitive to temperature, the temperature variations are twice as large in Model B.

The question addressed here is: where is post-perovskite predicted to occur in the

lowermost mantle for a model of temperature and compositional variations given a suite

of possible geotherms and Pv to pPv transition depths? We accomplish this by simply

adding the temperature variations from the thermo-chemical models to a mantle geotherm

18

to calculate the absolute temperatures. To obtain absolute values for iron, the variations

in the mole fraction of iron are added to the canonical value assumed for most of the

mantle, 0.1 [Ringwood, 1982; Jackson, 1998; Mattern et al., 2005]. Since the effects of

changes in silica content on the transition of perovskite to post-perovskite are not well

documented and the thermo-chemical models suggest that the effect of variations in silica

on seismic velocities in the lowermost mantle is secondary to that of temperature and

iron, the effects of the silica variations in the models are ignored. The resulting model of

absolute temperatures and values of the mole fraction of iron for the lowermost mantle is

then used to determine if the region would be in the perovskite or post-perovskite

stability field for a sampling of possible phase transition depths. Although current

experimental studies are in disagreement as to whether or not iron affects the depth of the

Pv to pPv transition [Mao et al., 2004, Hirose et al., 2006], neither Model A or B has

high enough iron fluctuations to affect the depth of the transition. The Mao et al. [2004]

study finds that as the mole fraction of iron increases the depth of the Pv to pPv transition

decreases. However, significant changes in depth do not occur until the mole fraction

surpasses approximately 15%. The largest absolute values of the mole fractions of iron

from Model A and B only approach 17% and 13% respectively. Therefore, for the

purposes of this study, the depth of the Pv to pPv transition is not affected by the

presence of iron.

While there is still disagreement regarding the depth of the Pv to pPv transition, to

date the experimental and theoretical mineral physics studies agree that the Clapeyron

slope of the transition is rather steep. Due to a limited number of data points in

experimental studies, the experimental Clapeyron slope of the transition is not well

19

constrained. However, theoretical studies are in agreement that the slope is positive and

in the range of 7 – 10 MPa/K [Tsuchiya et al., 2004a; Oganov and Ono, 2004]. Here the

determination of the presence of pPv is calculated using the preferred Tsuchiya et al.

[2004] slope of 7.5 MPa/K. Figure 9A shows the phase relationship between Pv and pPv

for the shallow and deep bounds of the Clapeyron slope given by Tsuchiya et al. [2004a]

(dashed lines) along with the Brown and Shankland [1981] geotherm (solid black line).

Figure 9B includes maps of perovskite (white) and post-perovskite (grey) in the bottom

layer of the mantle from the shallow (left) and deep (right) phase transitions in Figure 9A

for the model dominated by temperature variations (top row), and likewise the bottom

row is the result for the model dominated by variations in iron. When the shallow phase

transition is applied to both models, the lateral temperature variations are not large

enough to allow perovskite to be present such that the entire layer at the CMB is in the

post-perovskite stability field. Similarly, the lateral temperature variations are not large

enough to allow post-perovskite to be present in the case of the deep phase transition

such that the entire layer at the CMB is composed of perovskite for Model A. However,

the temperature variations are high enough in Model B for small amounts of post-

perovskite to be present when the deep transition is used. The previous discussion on

normal mode constraints concluded that post-perovskite is not a ubiquitous layer in the

lowermost mantle, so the upper bound on the transition depth is most likely too shallow,

hence an intermediate transition depth would be necessary to produce 3D variations.

This finding agrees with the assertion by Tsuchiya et al. [2004] that the upper and lower

bounds placed by their local density approximated (LDA) and generalized gradient

approximated (GGA) calculations are presumed to be unrealistic.

20

The presence of post-perovskite predicted for a suite of geotherms and transition

depths applied to the temperature-dominated Model A and the iron-dominated Model B is

shown Figures 10 - 12. In Figure 10A the Brown and Shankland [1981] geotherm and a

Clapeyron slope from Tsuchiya et al. (2004a) that intersects the geotherm at 2700° K are

shown. This mid-range phase transition predicts that post-perovskite will occur in the

cold regions of both Models A and B as demonstrated in Figure 10B. It is also possible

to have variations in the presence of pPv for other geotherms. Figure 11A shows the

upper and lower geotherms from Williams [1998]. The upper geotherm is calculated

assuming a 1000°K superadiabatic gradient across the transition zone, while the lower

geotherm assumes no superadiabatic gradient across the transition zone. For the low

geotherm, 3D variations in pPv occur if the phase transition is deep. As the geotherm in

the lower mantle increases, a shallower phase transition is necessary to obtain lateral

variations in pPv. Figure 12 shows similar results for the iron-dominated Model B. For

the purposes of this study, the main difference between Models A and B is that for a

given geotherm, the greater temperature fluctuations in Model B allow the phase

transition to occur at closer to the CMB and still produce 3D variations in post-

perovskite.

Since the tomographic models show that the fast anomalies in the lowermost

mantle appear over 500 km above the CMB (Figure 7), they are likely a thermal feature.

However, these fast velocities increase in magnitude at the CMB, suggesting an

additional component affecting seismic velocities at this depth. It is generally assumed

that the fast velocities at the CMB are due to the collective thermal and possibly chemical

variations of subducted slab material. The analysis of the seismically-derived thermo-

21

chemical models finds that the additional velocity increase in the circum Pacific near the

CMB could be due to the cold thermal anomalies shifting localized regions into the post-

perovskite stability field. Thus, the fast anomalies would be a combination of thermal

and mineralogical effects.

The observation of fast travel-time curves in slow regions of tomographic models

indicates that the iron content may vary locally on scales smaller than can be resolved by

seismic tomography. Even the low estimates of dlnVs/dXFe indicate that a 2% change in

shear velocity would be due to only a 0.08 change in the mole fraction of iron. Since the

estimates of dlnVs/dXFe are poorly constrained, it is possible that they are too high and

that the magnitude of iron variations is greater than that modeled here. Another

possibility is that there are very large fluctuations in iron content over distances of only a

few hundred kilometers that could lead to isolated pockets of post-perovskite. It may be

argued that post-perovskite would increase the shear velocity and thereby reduce the

magnitude of the slow seismic anomaly attributed to iron, resulting in an underestimate of

the relative increase in iron. However, the slow regions of the lowermost mantle are very

slow and very broad features, such that small pockets of post-perovskite will not affect

the regional velocity structure enough to substantially change the modeled variations in

iron content.

5. Conclusion

The current theoretical results suggest that the post-perovskite phase should have

a 2% increase in shear velocity and density compared to perovskite [Tsuchiya et al.,

2004a,b; Oganov and Ono, 2004], which is well within the detection threshold of long-

22

period seismic data. Therefore, this study systematically investigates the constraints that

long-period seismology can place on the ability of post-perovskite to exist in the

lowermost mantle. One possibility is that the lowermost mantle is cold enough that post-

perovskite is present as a global feature. Normal modes provide tight constraints on the

radial profile of velocity and density within the Earth and indicate that there is no global

increase in seismic velocity at depths shallower than 2680 km. At greater depths the

sensitivity of normal modes decreases such that a larger velocity increase would be

necessary in order to be resolved. The deeper the phase transition occurs, it becomes

more susceptible to lateral variations due the thermal and chemical heterogeneity

associated with the thermal boundary layer. Unfortunately the body wave coverage at

great depths is not globally uniform and therefore not as useful for determining the radial

seismic profile near the CMB. However, the body waves are capable of providing

detailed information in select areas that are sampled by a high density of turning rays.

Within a couple hundred kilometers of the CMB, body waves turning at these

depths are numerous enough in some regions that a seismic velocity jump would cause a

bend in the travel-time curve of S arrivals. A bend toward faster times representing a

velocity jump is found not only in tomographically fast regions beneath Eurasia and the

Cocos Plate, but also in tomographically slow regions such as the central Pacific. There

are more null observations in which no systematic shift in velocity is observed than there

are observations of fast or slow trends in the travel-time curves. Therefore, post-

perovskite is also not present as a global feature below 2680 km. The fast bends in the

travel-time curves consistently occur at approximately 100 km above the CMB and can

be attributed to velocity increases on the order of 0.5 – 1.0%. Although the temperature

23

rise at the CMB would likely cause pPv to revert back to Pv, a “double-crossing”

[Hernlund et al., 2005] of the phase boundary is beyond the resolution of this long-period

study. The presence of relatively fast material in the predominantly slow regions of the

lowermost mantle may reflect local temperature and/or chemical anomalies that are

favorable for the Pv to pPv transition. Thus, the long-period travel-times indicate the

presence of post-perovskite in a variety of localized regions of lowermost 100 km of the

mantle.

Having examined the effect of a variety of geotherms and depths of the Pv to pPv

transition for both a temperature and an iron dominated thermo-chemical model on the

presence of post-perovskite, a few characterizations can be made. First, the circum-

Pacific fast anomalies near the CMB can be explained by the combination of low

temperatures from subducting slabs and the subsequent transition to post-perovskite.

However, this is only possible for a very narrow range of mantle geotherms, transition

depths, and Clapeyron slopes. Thus, if one believes that post-perovskite is a major

contributor to these fast regions, then there exists a very tight constraint on the mantle

geotherm if the transition depth is known. Studies such as Hirose et al. [2006] and

Stackhouse et al. [2005b] suggest that chemistry does not greatly affect the depth of the

Pv to pPv transition, which if true, would indicate that the occurrence of post-perovskite

is mainly due to local temperature changes. In this study, the temperature model controls

the predicted locations of post-perovskite since the iron variations are not large enough to

affect the depth of the Pv to pPv transition even if it is assumed that the effect of iron is

substantial [Mao et al., 2004]. An increase in shear velocity consistent with the Pv to

pPv transition occurs in the travel-time curves at approximately 100 km above the CMB,

24

and is thus inconsistent with a superadiabatic mantle geotherm due to the shallow

transition depth required to obtain lateral variations in post-perovskite (Figures 11-12).

If the Clapeyron slope is known, which at this point, it is only reliably estimated from

theoretical studies, then the geotherm can be pinpointed once the depth of the Pv to pPv

transition is measured seismically. However, since there is currently no consensus as to

the exact depth or slope of the Pv to pPv transition, the tomographically derived thermo-

chemical models provide a means to narrow the range of possibilities. The predicted

occurrence of post-perovskite for both temperature models A and B suggest that the

mantle geotherm lies between 2400° K and 2700° K at approximately 100 km above the

CMB where the transition is observed in the travel-time curves. This result agrees with

the value of 2600°K at 2700 km depth reported by Ono and Oganov [2005].

Acknowledgements

The author would like to thank Alex Hutko for helpful advice for simplifying the

waveform analysis as well as Urska Manners and John Hernlund for thoughtful reviews

of the manuscript. Guy Masters provided the data for Figure 3, and Peter Shearer

provided the code to produce Figure 2A. This work was made possible with funding

distributed by the University of California Office of the President via the President’s

Postdoctoral Fellowship Program.

25

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Figure Captions

Figure 1: Western and Eastern Hemisphere views of the number of rays turning at

distances between 90° and 100° within 4° diameter bins. The scale is saturated in the

central Pacific where the number of rays exceeds 1000.

Figure 2: Top: Radiation pattern of fundamental modes 0S2

m and 0S4

m expressed as

spherical harmonics for !1 " m " 1. Bottom: Depth sensitivity of 0S2

m (bold lines) and

0S4

m (grey lines) as a function of radius where r = 1.0 at the Earth’s surface and

r = 0.55 at the CMB. The modes are dominantly sensitive to shear velocity structure

near the CMB.

Figure 3: Width of the mode resolution kernel for shear velocity (top), compressional

velocity (middle), and density (bottom) for anomalies of 0.1% (dashed line), 2.0% (solid

line), and 5.0% (dash-dot line) as a function of radius in the mantle. Generally resolution

width increases with depth, especially for shear velocity near the CMB. As the resolution

width increases it takes a larger magnitude anomaly to be within the mode threshold of

detection.

Figure 4: S wave arrival time picks made on synthetic seismograms calculated using

isotropic PREM (left) and an altered version of PREM with a 2% shear velocity increase

at 180 km above the CMB. The traces span from 80° – 100° with a 0.2° spacing and are

aligned on their PREM predicted times. The bend in the travel-time curve of the altered

PREM model begins at approximately 92°.

33

Figure 5: Geographic distribution of bins in which fast (blue), slow (red), or no (white)

trends is observed in the travel-time curve of long-period S arrivals. Areas outside of the

frame do not have the density of ray coverage to be used in this analysis. The clustering

of fast arrivals under Eurasia and the Cocos Plate may signal the presence of post-

perovskite.

Figure 6: Examples of the travel-time curves from bins in which a fast trend (left), no

trend (middle), or slow trend (right) is observed for long-period S wave arrivals. The

vertical yellow lines are provided as guides for determining the overall trend in the data.

Figure 7: Depth slices of the bottom 500 km of the shear velocity model, RMSL – S06,

from Reif et al. [2006]. Dark blues and reds are 2% fast and slow respectively. The

model is constrained near the CMB by the combination of direct S and core-reflected ScS

phases.

Figure 8: Depth slices of thermo-chemical models computed by applying different sets of

shear and compressional wave and density sensitivities to temperature and the mole

fractions of perovskite and iron in the lower mantle. The seismic and density data for

both models consist of a combination of body waves [Reif et al., 2006] and normal mode

splitting coefficients [Masters et al., 2000b]. Model A (top rows) uses the sensitivities of

Li [submitted] in which shear velocity is dominantly sensitive to temperature fluctuations.

34

Model B (bottom rows) uses the sensitivities of Trampert et al. [2004]. The scales of

both the temperature and chemical variations differ for the two models.

Figure 9: A: Phase diagram of the Pv to pPv transition assuming the Clapeyron slope of

7.5 MPa/K [Tsuchiya et al., 2004a] for the shallow limit (dashed line) and the deep limit

(dash-dot line). Also plotted is the Brown and Shankland [1981] geotherm (solid line).

B: Predicted locations of post-perovskite (grey) for the shallow transition (left) and the

deep transition (right) given the temperature dominated Model A (top) and iron

dominated Model B (bottom) shown in Figure 8.

Figure 10: A: Phase diagram of the Pv to pPv transition assuming the Clapeyron slope of

7.5 MPa/K [Tsuchiya et al., 2004a] for an intermediate depth that produces lateral

variation in the occurrence of post-perovskite using the Brown and Shankland [1981]

geotherm (solid line). B: Predicted location of post-perovskite given the temperature

dominated Model A (top) and iron dominated Model B (bottom) shown in Figure 8.

Figure 11: A: Phase diagram of the Pv to pPv transition assuming the Clapeyron slope of

7.5 MPa/K [Tsuchiya et al., 2004a] for a shallow transition (light dashed line) and a

deeper transition (bold dashed line). Also plotted are the adiabatic (bold solid line) and

superadiatic (light solid line) geotherms from Williams [1998]. B: The location of post-

perovskite (grey) assuming the adiabatic geotherm and deep phase transition (left) and

assuming the superadiabatic geotherm and shallow phase transition (right) given the

temperature anomalies from Model A.

35

Figure 12: A: Phase diagram of the Pv to pPv transition assuming the Clapeyron slope of

7.5 MPa/K [Tsuchiya et al., 2004a] for a shallow transition (light dashed line) and a

deeper transition (bold dashed line). Also plotted are the adiabatic (bold solid line) and

superadiatic (light solid line) geotherms from Williams [1998]. B: The location of post-

perovskite (grey) assuming the adiabatic geotherm and deep phase transition (left) and

assuming the superadiabatic geotherm and shallow phase transition (right) given the

temperature anomalies from Model B.

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Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

42

Figure 7

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Figure 8

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Figure 9

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Figure 10

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Figure 11

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Figure 12